Question

You are analyzing a manufacturing process and determine that 1% of the parts do not meet specifications (they are non-conforming). If you take a random sample of 50 parts from this process, what is the probability that 2 or more will be non-conforming?

Answer 1

Here sample size is large and probability of the items which do not meet specifications is very small as 0.01

So we can use Poisson distribution to find the probability.

Let X = number of items  which do not meet specifications.

So X follows Poisson distribution with parameter   $\lambda$ = n*p = 50 * 0.01 = 0.5

Here we want to find P( X >= 2) = 1 - P( X <= 1) ......( 1 )

Let's use excel:

P( X <= 1) = "=POISSON(1,0.5,1)" = 0.9098

Plug this value in equation ( 1 ), we get:

P( X >= 2) = 1 - 0.9098 = 0.0902 ( This is the final answer).